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1

Improved Modeling of Loading Kinetics in

Detailed Filter Media Simulations with

GeoDict

Jürgen Becker, Andreas Wiegmann

Math2Market GmbH, Kaiserslautern, Germany

Friedemann Hahn, Uwe Staudacher, Martin J. Lehmann

MANN+HUMMEL GMBH, Ludwigsburg, Germany

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Overview

1. Motivation - peculiar effects observed in experiments

2. Hypothetical explanations

3. Filtration simulation with GeoDict

4. Results

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1. Experimental Observations

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The Multipass Test (ISO 4548)

Storage vessel

Contamination circuit

Testing circuit

Dilution system

Particle injection

Pump

Filter

Qp

Qinj

Pressure sensor

Pressure sensor Online particle counter 2

Online particle counter 1

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The Multipass Test (ISO 4548)

Initial efficiency Cake filtration

How to understand

what‘s going on here!?

Elapsed time [min]

Filt

er

effic

iency [

%]

100

80

60

40

20

0 0 10 20 30 40 50 60 70 80

d ~ 15 µm

d ~ 9 µm

Simulation

(GeoDict

2012R1)

Testing

Peculiarities observed in testing of depth filter media

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2. Hypothetical Explanations

for a Decreasing Efficiency

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Explanation A: Re-Entrainment

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Explanation B: Lingering

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Explanation C: Flow Pathways

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3. General Approach

to Filtration Simulations

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Filter Simulation: Efficiency

Basic idea:

1. Filter model

2. Determine flow field

3. Track particles (filtered or not?)

Randomness:

Starting positions

Brownian motion

Result:

Percentage of filtered particles

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Tracking the Particles

No interaction between particles

Flow field is not changed by a moving particle

Modeled effects:

Inertia

Brownian motion

Electrostatic attraction or repulsion

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Adhesion Model

What happens when a particle hits the filter material?

a) sticks to material (deposited)

b) bounces off

Particles always stick => Caught on first touch model

Particles always bounce off => Sieving model

Particles loose energy when bouncing => Restitution factor

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Hamaker Model

Adhesive forces:

(van-der-Waals forces between spherical particle and flat surface)

H Hamaker constant [J]

d Particle diameter

a Distance between particle and surface

Escape velocity:

1. Integrate from a0 (min distance = 4e-10) to infinity

2. Compare with kin. energy of particle

2

2

04

Hv

a r

212vdW

HdF

a

Particle sticks for smaller velocities v.

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Comparison

Caught on first touch Sieving Hamaker

H =1e-21

Restitution = 0.5

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Filter Simulation: Life Time

1. Filter Model

6. Repeat ... 5. Flow Field 4. Deposit Particles

2. Flow Field 3. Track Particles

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Improvements to FilterDict

Global time concept: particles can continue to the next batch

=> allows lingering particles

=> needed for re-entrainment

More accurate particle tracking

2012R1:

flow solver uses staggered grid but writes cell-centered result file

particle tracking uses cell-centered file

=> accuracy lost (especially at no-slip boundary)

2012R2:

flow solver uses staggered grid and writes staggered grid result file

particle tracking uses staggered grid

...

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Effect of Higher Accuracy:

MPPS Simulation Example

Structure:

Fibers with diameter 20 µm

Different porosities

Different resolutions (voxel length 1 µm – 4µm)

Simulation:

Find efficiency for all particle diameters

(caught on first touch, air filtration)

Brownian Motion: on/off

Inertia: on/off (by particle weight)

Different flow velocities

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Fixed: Porosity 90%, Resolution 2 µm

Vary: Velocity

0.00 %

10.00 %

20.00 %

30.00 %

40.00 %

50.00 %

60.00 %

70.00 %

80.00 %

90.00 %

100.00 %

0.001 µm 0.01 µm 0.1 µm 1.0 µm 10.0 µm 100.0 µm

v0.02

v0.02 Inertia + Diffusion

v0.2

v0.2 Inertia + Diffusion

Should be zero!

But: Interpolation

error!

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Enhancement of Interpolation in 2012R2

0.00 %

10.00 %

20.00 %

30.00 %

40.00 %

50.00 %

60.00 %

70.00 %

80.00 %

90.00 %

100.00 %

0.001 µm 0.01 µm 0.1 µm 1.0 µm 10.0 µm 100.0 µm

r1

r1 center

r1.5

r1.5 center

r2

r2 center

r3

r3 center

r4

r4 center

2012 R1: Interpolation from

cell-centered velocities

2012 R2: Interpolation from

original staggered grid

Voxel length 3 µm in 2012R2

same quality as

Voxel length 2 µm in 2012R1

200x200x200 (=8 Mio) in 2012R2

same quality as

300x300x300 (=27 Mio) in 2012R1

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4. Results

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Decreasing Efficiency by Changed Pathways

0 %

10 %

20 %

30 %

40 %

50 %

60 %

0 1000 2000 3000 4000 5000

To

tal F

iltr

ati

on

Eff

icie

nc

y

Time / s

Total Filtration Efficiency by Weight

=> Effect can explain

decreasing efficiencies!

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Reentrainment & Lingering

Observations from numerous simulations:

Larger particles get sieved!

Local flow field does not flip direction => particles stay sieved.

=> Larger particles do not re-entrain (in significant numbers)!

Initially, particles pass the clean filter quickly.

Small particles pass through filter cake slowly

(in later stages of filtration, assuming sieving model)

=> This is most likely not the main explanation!

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Flow

Simulation Results

(GeoDict 2012R2 Version)

Tomography cut-out

Oil filtration

Adhesion model: sieving

No re-entrainment

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0 %

10 %

20 %

30 %

40 %

50 %

60 %

70 %

80 %

90 %

100 %

0 200 400 600 800 1000 1200 1400 1600 1800 2000

To

tal F

iltr

ati

on

Eff

icie

nc

y

Time / s

resolution 1 µm

resolution 2 µm

Total Efficiency by Weight

Efficiency is initially

decreasing!

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Fractional Filtration Efficiency

0.00 %

10.00 %

20.00 %

30.00 %

40.00 %

50.00 %

60.00 %

70.00 %

80.00 %

90.00 %

100.00 %

0 s 500 s 1000 s 1500 s 2000 s

1 µm

5 µm

9 µm

15 µm

25 µm

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Summary and Outlook

Summary:

Decreasing efficiencies can be explained by simulation

=> No re-entrainment, but explained geometrically

Improvements needed:

More accurate particle tracking / flow field interpolation

Global time concept: particles can continue in the next batch

Future improvements:

Enhance fractional efficiency determination (Filtech 2013)

Reconsider sieving criterion w.r.t. resolution dependency

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Thank You !

The Virtual Material Laboratory www.geodict.com